Satanic comma

The satanic comma (monzo: [-1054 665⟩) is the difference between 666 perfect fifths (octave-reduced) and a single perfect fifth. Equivalently, it is the difference between 665 perfect fifths (octave-reduced) and the unison – but that would not be as devilishly intriguing. This difference is inaudible, at only 0.076 ¢.

Interval information

Factorization	2-1054 × 3665
Monzo	[-1054 665⟩
Size in cents	0.07557548¢
Name	satanic comma
FJS name	[math]\displaystyle{ \text{95d}{-64} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	2108
Weil norm (log2 max(n, d))	2108
Wilson norm (sopfr(nd))	4103
Comma size	unnoticeable
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It is also the difference between 13 Mercator's commas and 2 pythagorean commas, or put another way, the difference between 11 pythagorean commas and 13 countercomp commas.

It is tempered out in 665edo and its multiples (1330edo, etc.), with 665edo itself being an 11-strong 3-2 telic system due to tempering this comma out. The next smallest 3-limit comma is the 190537-comma, which is orders of magnitude much smaller and complex.

Etymology

This comma was named by Marc Jones in 1990.